The present invention relates generally to 3-D surface measurement systems and methods, and more particularly, a system and method for determining Planar Path lengths along a surface of a 3-D object.
Pathfinding allows access to important spatial information such as the path length and shape along an object""s surface between two points. Measuring the Euclidean distance (ED) between two points in the Euclidean space coordinate is a common measurement procedure in industrial and medical applications. This measurement represents the shortest linear path between the two points. However, if the desired path between the two points is not linear then the ED does not provide an accurate length.
The difficulty is not how to measure the length of a curve confined between two points; rather, the difficulty is how to find a curve that satisfies a special relationship between two points. For instance, finding the shortest path between two points along a non-planar three-dimensional surface is difficult. An infinite number of curves exist between the two points. These curves can be planar or non-planar. In addition, determining the shortest path between the two points adds complexity to the problem. One common solution is to manually outline the expected shortest path. This manual technique is time consuming and tedious, especially when the two points cannot be viewed simultaneously. More importantly, although the accuracy may be acceptable, the precision of the manual technique is poor and user dependent.
Therefore, a more precise method of determining the shortest path between two points located on a three-dimensional surface (geodesic) in an unsupervised manner and timely fashion is needed. Such a technique would be applicable to inspection techniques for measuring the dimensions of mechanical parts or other similar structures.
The present invention provides a system for performing three-dimensional surface measurements that substantially eliminates or reduces disadvantages and problems associated with previously developed surface measurement techniques.
More specifically, the present invention provides a method for path length determination along the surface of a three-dimensional object. The method for determining the path length along the surface of a three-dimensional geodesic includes the steps of first selecting a first and second point on the three-dimensional surface. A plane is then defined which contains both the first and second points. The intersection of the three-dimensional object with the plane defines the shortest path curve between the first point and second point. This path length is recorded for future comparison. A series of subsequent planes is defined that contains the first and second point, wherein these planes are oriented at an angle to the previous planes. A determination is then made for the shortest path length associated with each subsequent plane. The overall shortest path length is the minimum recorded path length from all planes examined.
The present invention provides an important technical advantage in that a computer system can be constructed that is operable to execute a set of instructions using the methods provided by vector calculus, in an unsupervised manner, to determine the minimum path lengths for any given geodesic examined with the method of the present invention.
More importantly, the present invention provides a key technical advantage in that prior art systems relied on inaccurate manual techniques, while the present invention eliminates these user-dependent manual techniques in favor of a computer-supervised measurement system. The method of the present invention eliminates precision errors associated with manual techniques of prior art systems.
The method of the present invention provides yet another important technical advantage in that the method of the present invention can be executed by an unsupervised computer system wherein the computer is operable to evaluate all path lengths in a timely fashion.